A material is proposed as an essential abrasive component for cleaning agents in cleaning products for delicate surfaces which is essentially composed of platelets. These platelets are preferably shaped without sharp points, i.e. their circumference is similar to a polygon whose corners do not show angles that are in the majority smaller than 30.degree. and greater than 330.degree.. Glass flakes are for example such a material. The abrasive component of the invention may for example be used for the manufacture of toothpastes and prophylaxis pastes that are efficient but nevertheless not harmful to teeth.